Mathematics Academy

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July 7 - July 27, 2019

Math Academy

The Mathematics Academy is a unique opportunity for students interested in examining mathematical concepts rarely offered at the high school level. This rigorous, proof-oriented program will fuse lectures, problem sessions, demonstrations, and exploratory research to engage students in topics such as:

Discrete Mathematics
  • Combinatorics (enumerative, algebraic and geometric)
  • Generating functions and partitions
  • Graph theory
  • Probability
  • Combinational game theory
Algebra and Number Theory
  • Linear algebra
  • Prime and factorization algorithms
  • Congruencies and quadratic reciprocity
  • Galois theory
  • Geometry of numbers
Geometry and Topology
  • Euclidean and non-Euclidean geometries
  • Geometric transformations
  • Algebraic geometry
  • Point-set topology
  • Knot theory

If you attend a School District of Philadelphia public or charter high school, you may be eligible to attend a Penn Summer Academy free of charge with a Penn Summer Scholarship.

Get application information >



Lectures and discussions: Attend sessions with mathematics faculty and experts which include lectures, recitations, group work, computer simulations, and problem sessions.

Field trips: Explore mathematical concepts in museums and other learning centers. Past field trips have included the National Museum of Mathematics in New York City, the National Cryptologic Museum in Maryland, and an M.C. Escher exhibition in Brooklyn.

Comprehensive mathematics: Explore topics such as combinatorics, generating functions and partitions, graph theory, probability, combinational game theory, Galois theory, linear algebra, prime and factorization algorithms, congruencies and quadratic reciprocity, geometry of numbers, Euclidean and non-Euclidean geometries, geometric transformations, algebraic geometry, point-set topology, and knot theory.

See this program’s 2018 syllabus.

Prerequisite: One year of high school Algebra II/Trigonometry is required for application.

Penn Summer High School

tuition and fees


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Penn Summer

3440 Market Street, Suite 100
Philadelphia, PA 19104-3335

(215) 898-7326

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